Least Common Multiple (LCM) of 61 and 164
The least common multiple (LCM) of 61 and 164 is 10004.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 61 and 164?
First, calculate the GCD of 61 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 164 = 0 remainder 61 |
| 2 | 164 ÷ 61 = 2 remainder 42 |
| 3 | 61 ÷ 42 = 1 remainder 19 |
| 4 | 42 ÷ 19 = 2 remainder 4 |
| 5 | 19 ÷ 4 = 4 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 141 and 114 | 5358 |
| 181 and 165 | 29865 |
| 146 and 107 | 15622 |
| 53 and 144 | 7632 |
| 160 and 170 | 2720 |